Condition for unique solution

CBSE 2026 30/8/1 · MATH · Easy · Pair of Linear Equations in Two Variables · MCQ · 1 mark

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The pair of linear equations $5kx + 3y = 7$ and $4x - 3y = k$ has unique solution, if :

A.
$k = 0$
B.
$k \neq -\frac{4}{5}$
C.
$k \neq -\frac{5}{4}$
D.
$k = -\frac{4}{5}$

Answer

B

Explanation

For a pair of linear equations to have a unique solution, $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$ .

Here $a_1 = 5k, b_1 = 3, a_2 = 4, b_2 = -3$ .

$\frac{5k}{4} \neq \frac{3}{-3} = -1 \implies 5k \neq -4 \implies k \neq -\frac{4}{5}$

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